The treatment of certain diseases of the central nervous system (Alzheimer, Huntington disease, etc) require the insertion of therapeutic drug molecules directly into the porous tissue of target areas deep in the brain. The design of invasive drug delivery therapies [Nicholson, 1985] constitutes a challenging transport problem with complex metabolic drug-neural interaction. The efficiency of th...

In this paper, first a great number of inverse problems which arise in instrumentation, in computer imaging systems and in computer vision are presented. Then a common general forward modeling for them is given and the corresponding inversion problem is presented. Then, after showing the inadequacy of the classical analytical and least square methods for these ill posed inverse problems, a Baye...

Inversion and PDE-constrained optimization problems often rely on solving the adjoint problem to calculate the gradient of the objective function. This requires storing large amounts of intermediate data, setting a limit to the largest problem that might be solved with a given amount of memory available. Checkpointing is an approach that can reduce the amount of memory required by redoing parts...

Inversion based on L2 norm has been widely used in geophysical problems. However, L2 inversion is only capable of recovering smooth features. To obtain sharp boundaries, non-L2 inversion has been used successfully. In reality, however, both smooth and blocky features can be present in the subsurface physical property or interfaces to be recovered. To deal with this situation, we propose a new m...

We consider the pseudo-inversion operation inspired by a biological event as a result of the partial inversion. We define the pseudoinversion of a string w = uxv to consist of all strings vxu, where uv = λ and consider the operation from a formal language theoretic viewpoint. We show that regular languages are closed under the pseudoinversion operation whereas context-free languages are not. Fu...

Interpretation of potential and electromagnetic (EM) fields observed over 3D geological structures remains one of the most challenging problems of exploration geophysics. In this paper I present an overview of modern methods of inversion and imaging of gravity, magnetic, and EM data, which are based on new advances in regularization theory related to application of special stabilizing functiona...

We propose a machine learning approach to geophysical inversion problems for the exploration of earth resources. Our approach is based on nonparametric Bayesian methods, specifically, Gaussian processes, and provides a full distribution over the predicted geophysical properties whilst enabling the incorporation of data from different modalities. We assess our method both qualitatively and quant...

In contrast to mono-constrained flows with N degrees of freedom, binary constrained flows of soliton equations, admitting 2 × 2 Lax matrices, have 2N degrees of freedom. By means of the existing method, Lax matrices only yield the first N pairs of canonical separated variables. An approach for constructing the second N pairs of canonical separated variables with additional N separated equations...

This work is devoted to the theory of joint interpretation of multimethod geophysical data and its application to the solution of real geophysical inverse problems. The targets of such joint interpretation can be geological bodies with an established dependence between various physical properties that cause anomalies in several geophysical fields (geophysical multiresponse). The establishing of...

This note describes an interferometric reformulation of linear wave-based inverse problems, such as inverse source and inverse Born scattering. Instead of fitting data directly, we propose to match cross-correlations and other quadratic data combinations that generalize cross-correlations. This modification exhibits surprising robustness to modeling uncertainties of a kinematic nature. Three op...